Question

Conduct a hypothesis testing on the slope coefficient to find if there is a meaningful correlation between Earnings and Years Education variables under 5% significance level and 95% CI.

There is a research whether more years of education has positive impact on average hourly earnings.????????(!=−7.29+1.96∗??????????????R2 = 0.35, SER =2.5(2.3) (0.5)

Answer 1

Test statistic = coefficient / standard error

= 1.96/0.5 = 3.92

Z critical value at 5% level of significance = 1.96

SInce, 3.92 > 1.96, the test statistic is greater than the Z critical value and thus coefficient on years of education is significant and the null hypothesis of 0 correlation can be rejected

95% confidence interval is as follows:

Upper limit = coefficient + standard error*Z-critical value = 1.96 + 0.5*1.96 = 2.94

Lower limit = coefficient - standard error*Z-critical value = 1.96 - 0.5*1.96 = 0.98

since 0 does not lie in the confidence interval, coefficient on years of education is significant and the null hypothesis of 0 correlation can be rejected